I assume they had common ownership. Doesn't seem likely the owner of the Belmont would want to pop for matches advocating the Adolphus if he had no interest in the place. But there's no mention of any chain. Thought it could've been the Massaglia Hotel chain, which was one of the owners of the New Yorker, but they bought it after the Book-Cadillac was renamed.

Finally found the answer: it was part of the National Hotel Management Company, the head of which was Ralph Hitz.

He died in 1939, and the company was dissolved within the year. This unremarkable document is one of the older ones in the collection.